Three repayment structures, one balance
Every federal Direct Loan borrower starts on the standard plan unless they choose otherwise: level payments over ten years, computed with the ordinary amortised-loan formula. It produces the highest payment and the lowest total interest of the three plans here, and it is the plan against which the others should be judged.
Extended repayment stretches level payments over up to 25 years and is available to Direct Loan borrowers with more than $30,000 outstanding. The payment falls sharply and the interest rises sharply — on a $35,000 balance at 6.53%, moving from ten years to twenty-five cuts the payment from $397.95 to $236.98 and raises total interest from $12,754 to $36,094.
Graduated repayment keeps the ten-year term by default but starts the payment low and steps it up every two years, on the theory that your income will rise. Federal rules constrain it: payments must increase, and no payment may be more than three times any other. The starting payment is lower than standard and the total interest is higher, because more of the balance stays outstanding for longer.
Income-driven plans exist too and work on a different principle entirely — payment as a percentage of discretionary income, with forgiveness after a period of qualifying payments. They cannot be priced from a balance and a rate alone, so they are not modelled here.
How each plan is priced, and what capitalisation does
Standard and extended use the same identity as a mortgage: M = B·r / (1 − (1 + r)−n), with the monthly rate r and the number of payments n. The only difference between the two plans is n.
Graduated needs a present-value condition instead of a formula. The payment in month k is M0(1 + g)⌊k/24⌋ — the starting payment multiplied by the step-up once for each completed two-year block. Setting the present value of that whole stream equal to the balance and solving for M0 gives the starting payment. With a 15% step over ten years there are five blocks, so the final payment is 1.154 = 1.749006 times the first, comfortably inside the three-times limit.
Capitalisation is the part borrowers most often miss. Federal loans accrue simple daily interest on outstanding principal. On unsubsidised loans that accrual continues through school, grace and most deferments — and when repayment begins, the accrued interest is capitalised: added to principal, where it then earns interest itself. Six months of grace at 6% turns a $20,000 balance into $20,600, and every payment for the next ten years is computed on the larger figure. Paying the accrued interest before it capitalises is one of the highest-return moves available to a new graduate.
Worked example: $35,000 at 6.53% on the standard plan
Take the defaults — $35,000 of loans at a 6.53% weighted average rate, no grace-period accrual, standard ten-year repayment.
- Monthly rate. 6.53 ÷ 1,200 = 0.005441667.
- Number of payments. 10 × 12 = 120.
- Discount factor. (1.005441667)120 = 1.9178978, so (1 + r)−120 = 0.5214042 and 1 − that = 0.4785958.
- Payment. 35,000 × 0.005441667 ÷ 0.4785958 = 190.458 ÷ 0.4785958 = $397.95.
- Total repaid. 120 × 397.9524 = $47,754.28.
- Total interest. 47,754.28 − 35,000 = $12,754.28, which is 26.7% of everything you repay.
Now price the same balance three other ways. Extended over 20 years: $261.57 a month and $27,777 of interest. Extended over 25 years: $236.98 a month and $36,094 of interest. Graduated over ten years with 15% steps: starting at $306.01, ending at $535.21, and costing $14,518 in interest.
The comparison to hold on to is the 25-year extended plan: it saves $160.97 a month against standard and costs $23,340 more in interest. Whether that is a good trade depends entirely on what the freed cash flow does — clearing a 22% credit card with it is clearly worth it, and simply absorbing it into spending clearly is not.
Choosing a plan, and what the payment does not tell you
Read the interest share before the payment. It is total interest divided by everything you repay, and it turns a plan choice into one comparable number: 26.7% on the ten-year standard plan in the example above, and 50.7% on the 25-year extended plan — meaning half of every dollar you send goes to interest rather than to the debt.
Choose the shortest plan whose payment you can actually sustain. A missed payment is far more costly than a longer term, because federal delinquency and default carry consequences no private loan does: wage garnishment without a court order, offset of tax refunds and Social Security payments, and loss of eligibility for further aid. If the standard payment is genuinely unaffordable, the right first step is usually an income-driven plan rather than an extended one, because income-driven payments fall with income and carry forgiveness at the end.
Beware of the graduated plan's shape. The starting payment is the number people compare, and it is the least informative one: the payment rises 15% every two years and the final block is nearly 1.75 times the first. Take it if you have a specific reason to expect income growth — a residency, a clerkship, a training contract — and not merely because the first year looks easier.
Finally, note what prepayment does here. Federal loans carry no prepayment penalty, and any extra money goes to outstanding interest first and then to principal. Because interest accrues daily on principal, an extra payment made early is worth more than the same payment made later — the same mechanism as the mortgage extra payment calculator, at a shorter horizon.
Monthly payment per $10,000 borrowed
| Rate | 10 years | 15 years | 20 years | 25 years |
|---|---|---|---|---|
| 3% | $96.56 | $69.06 | $55.46 | $47.42 |
| 4% | $101.25 | $73.97 | $60.60 | $52.78 |
| 5% | $106.07 | $79.08 | $66.00 | $58.46 |
| 6% | $111.02 | $84.39 | $71.64 | $64.43 |
| 7% | $116.11 | $89.88 | $77.53 | $70.68 |
| 8% | $121.33 | $95.57 | $83.64 | $77.18 |
Doubling the term never halves the payment: at 6% the 20-year payment is 64.5% of the 10-year one, not 50%, because the extra decade of interest has to be paid for. The gap widens as the rate rises — at 8% the same ratio is 68.9%.
What this calculator does not model
- Income-driven repayment. SAVE, IBR, PAYE and ICR set payments from discretionary income and family size, not from the balance, and carry forgiveness after a qualifying period. They cannot be priced from a rate and a balance.
- Public Service Loan Forgiveness. PSLF discharges the remaining balance after 120 qualifying payments in eligible employment, which changes the optimal strategy completely — under PSLF you want the lowest qualifying payment, not the fastest payoff.
- Subsidised versus unsubsidised. Interest does not accrue on subsidised loans during school, grace or approved deferment. Set the grace months to zero for the subsidised portion of your balance.
- Consolidation mechanics. A Direct Consolidation Loan takes the weighted average of your rates rounded up to the nearest one-eighth of a percentage point, and resets progress towards forgiveness. It lengthens the term rather than lowering the rate.
- Private loans. These have their own terms and none of the federal protections. A private loan at a lower rate is not automatically better than a federal one at a higher rate.
- Interest rate changes. Federal rates are fixed for the life of each loan but set annually for new loans, so a balance built over several years is a blend of different rates. Use the weighted average.
- Tax treatment. Student loan interest may be deductible up to a limit, subject to income phase-outs; that deduction is not modelled here.
Where student debt sits in a household plan
Federal student loans are unusual debt. They are unsecured but survive bankruptcy in almost all cases; they carry hardship protections no other consumer loan offers; and they can be forgiven under specific programmes. That mix of features means the usual rule — clear the highest rate first — has an important exception for federal loans, because the optionality is worth something the rate does not capture.
The ordering that generally holds: take any employer retirement match first, clear credit-card debt next since the rate gap is enormous, then decide between student loans and other goals. The debt avalanche calculator handles the ordering when several balances compete, and the credit card payoff calculator prices the balance that is usually the most expensive one you hold.
Two forward-looking points. A student loan payment reduces the mortgage you qualify for — at a 6.5% thirty-year rate, every $1 of monthly debt payment costs about $158 of mortgage capacity, so the default $397.95 payment removes roughly $63,000 of it. Run the home affordability calculator with the real payment in the debts field before assuming otherwise. And if you are on the other side of this — saving for a child's education rather than repaying your own — the 529 college savings calculator sizes the contribution that reduces how much of this any of you has to borrow.